Meso-scale models and approximate solutions for solids containing clouds of voids

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved in the description of the geometry of the domain. The size of the perforations is small compared to the minimal separation between neighbouring defects and here we discuss a class of problems in perforated domains, which are not covered by the homogenisation approximations. The meso-scale approximations presented here are uniform. Explicit asymptotic formulae are supplied with the remainder estimates.